question_answer

A force 20 N acts on a cube producing an acceleration of \[5\,m/{{s}^{2}}\]. Find the density of the material of the cube, if its volume is \[\text{1 }{{\text{m}}^{\text{3}}}\]?

Answer:

Force acting on a cube, \[F=20\,\,N\] density of the cube, d = ? Acceleration produced, \[a=5m/{{s}^{2}}\] Volume of the cube,\[V=1\,{{m}^{3}}\] We know that, \[density(d)=\frac{mass(m)}{Volume(V)}\Rightarrow d=\frac{{}^{F}/{}_{a}}{V}\] \[\left[ \because F=ma\Rightarrow m=\frac{F}{a} \right]\] \[\therefore d=\left( \frac{F}{a\times V} \right)=\frac{20}{5\times 1}=4\,\,kg/{{m}^{3}}\] Newton?s Second Law of motion can also be derived from the momentum of a body.